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Ann Occup Hyg. 2015 Jul;59(6):764-74. doi: 10.1093/annhyg/mev011. Epub 2015 Mar 6.

Log-Linear Modeling of Agreement among Expert Exposure Assessors.

Author information

1.Retrospective Observation Studies, Evidera, 430 Bedford St, Suite 300, Lexington, MA 02420, USA
2.Occupational and Environmental Epidemiology Branch, Division of Cancer Epidemiology and Genetics, National Cancer Institute, 9609 Medical Center Drive, Bethesda, MD 20892, USA.
3.Work Environment Department, University of Massachusetts Lowell, One University Avenue, Lowell, MA 01854, USA.
4.School of Mathematical Sciences, University of Technology Sidney, 15 Broadway, Ultimo, NSW 2007, Australia.
5.Maryland Institute for Applied Environmental Health, University of Maryland School of Public Health, 2234V School of Public Health, College Park, Maryland 20742, USA.



Evaluation of expert assessment of exposure depends, in the absence of a validation measurement, upon measures of agreement among the expert raters. Agreement is typically measured using Cohen's Kappa statistic, however, there are some well-known limitations to this approach. We demonstrate an alternate method that uses log-linear models designed to model agreement. These models contain parameters that distinguish between exact agreement (diagonals of agreement matrix) and non-exact associations (off-diagonals). In addition, they can incorporate covariates to examine whether agreement differs across strata.


We applied these models to evaluate agreement among expert ratings of exposure to sensitizers (none, likely, high) in a study of occupational asthma.


Traditional analyses using weighted kappa suggested potential differences in agreement by blue/white collar jobs and office/non-office jobs, but not case/control status. However, the evaluation of the covariates and their interaction terms in log-linear models found no differences in agreement with these covariates and provided evidence that the differences observed using kappa were the result of marginal differences in the distribution of ratings rather than differences in agreement. Differences in agreement were predicted across the exposure scale, with the likely moderately exposed category more difficult for the experts to differentiate from the highly exposed category than from the unexposed category.


The log-linear models provided valuable information about patterns of agreement and the structure of the data that were not revealed in analyses using kappa. The models' lack of dependence on marginal distributions and the ease of evaluating covariates allow reliable detection of observational bias in exposure data.


asthma; epidemiology; expert judgement; exposure assessment methodology; sensitization

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